Journal of Food Engineering 52 (2002) 349–357 www.elsevier.com/locate/jfoodeng

Thin-layer modelling of black tea drying process
P.C. Panchariya a, D. Popovic b b,*

, A.L. Sharma

c

a Central Electronics Engineering Research Institute, Pilani 333031, India Institute of Automation Techniques, University of Bremen, D-28359, Bremen, Germany c Institute of Instrumentation, D.A. University, Khandwa Road, Indore 452017, India

Received 16 March 2001; accepted 25 June 2001

Abstract An experimental dryer was developed for determining the kinetics of black tea drying. Drying characteristics of tea were examined using heated ambient air for the temperature range 80–120°C and air flow velocity range 0.25–0.65 m/s. The data of sample weight, dry- and wet-bulb temperatures and air velocity of the drying air were recorded continuously during each test. The drying data were then fitted to the different semi-theoretical models such as Lewis, Page, modified Page, two-term and Henderson and Pabis models, based on the ratios of the difference between the initial and final moisture contents and the equilibrium moisture content. The Lewis model gave better predictions than other models, and satisfactorily described the thin-layer drying characteristics of black tea particles. The effective diffusivity varied from 1:14 Â 10À11 to 2:98 Â 10À11 m2 /s over the temperature range. The temperature dependence of the diffusivity coefficient was described by the Arrhenius-type relationship. The activation energy for moisture diffusion was found to be 406.02 kJ/mol. Temperature and air velocity dependence on drying constant was described by the Arrheniustype and Power-type relationships. The coefficients of determination were above 0.996 for both relationships. The Arrhenius-type model was used to predict the acceptable moisture ratios at the experimental drying conditions and to understand better the influence of drying variables on drying rate constant. The results illustrate that in spite of high initial moisture content, the drying of tea particles takes place only in the falling rate period. This single-layer drying equation can be used for the simulation of deep-bed drying of black tea. Ó 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Thin-layer; Dhool; Moisture ratio; Non-linear regression; Predictions

1. Introduction India is the largest producer of black cutting, tearing, and curling (CTC) tea with a distinct characteristic, taste, and flavour. The tea leaves, after being plucked from the tea bush, go through various processing stages, such as withering, CTC, fermentation, drying, and finally packing. The drying operation in the tea industry does not merely remove the moisture content because there are many quality factors which can be adversely affected by incorrect selection of drying conditions and drying equipments. The consumer acceptability, appearance and organoleptic properties are the desirable properties of high-quality tea. To design and control a tea dryer and to define optimum drying conditions, it is necessary to model the

Corresponding author. Tel.:+49-421-218-3580; fax: +49-421-2184707. E-mail address: popovic@iat.uni-bremen.de (D. Popovic).

*

actual process of drying in terms of mathematical relations. In the actual operation, black tea is dried in various types of deep-bed dryers. Due to its complexity, it is difficult to investigate the drying characteristics of an actual industrial drying bed directly. In our case the actual deep-bed drying is analysed using process state values such as drying air temperature, moisture content, etc. that are calculated from heat and mass balance of the drying process represented as a thin-layer drying model. Although in the past many theoretical and empirical models were developed for various foods and agro-based products (Basunia & Abe, 2001; Can, 2000; Kiranoudis, Maroulis, Tasami, & Marinos-Kouris, 1997), none of the works reported on Darjeeling black tea. Thus, the objective of this study was the development of a suitable experimental thin-layer drying apparatus, to find out suitable model and to investigate the effect of temperature and air velocity on the model coefficients which can describe the drying characteristics of black tea particles.

0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 1 ) 0 0 1 2 6 - 1

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Notation a; b drying constant A; A0 ; A1 drying constant c; c0 ; c1 drying constant Deff effective diffusivity (m/s) D0 diffusivity coefficient Ea activation energy (kJ/mol) k; k0 ; k1 drying constant M moisture content MR moisture ratio R2 R t T correlation coefficient universal gas constant time (s) temperature

Subscripts i ith observation 0 initial e equilibrium

2. Mathematical modelling It has been accepted that drying phenomenon of biological products during the falling rate period is controlled by the mechanism of liquid and/or vapour diffusion. Thin-layer drying models that describe the drying phenomenon of these materials mainly fall into three categories namely, theoretical, semi-theoretical and empirical. The first takes into account only internal resistance to moisture transfer while the other two consider only external resistance to moisture transfer resistance between product and air (Fortes & Okos, 1981; Henderson, 1974; Whitaker, Barre, & Hamdy, 1969). Assuming that the resistance to moisture flow is uniformly distributed throughout the interior of the homogeneous isotropic material, the diffusion coefficient, D is independent of the local moisture content and if the volume shrinkage is negligible, Fick’s second law can be derived as follows: oM ¼ Dr2 M: ot ð1Þ

(3)), the Lewis model (Eq. (5)), the Page model (Eq. (6)) and the modified Page model (Eq. (7)) are used widely. Sharaf-Eldeen, Blaisdell, and Hamdy (1980) presented a two-term model to predict the drying rate of shelled corn fully exposed to air. This model is the first two terms of general series solution to the analytical solution of Eq. (1). However, it requires constant product temperature and assumes constant diffusivity. The two-term exponential model has the form MR ¼ M À Me ¼ A0 expðÀk0 tÞ þ A1 expðÀk1 tÞ; M0 À Me ð2Þ

where M, M0 and Me are the material, initial, and equilibrium moisture contents in dry basis, respectively, and A0 ; k0 ; A1 ; k1 are the empirical coefficients. The Henderson and Pabis model is the first term of a general series solution of Fick’s second law (Henderson & Pabis, 1969) MR ¼ M À Me ¼ A0 expðÀk0 tÞ: M0 À Me ð3Þ

Crank (1975) gave the analytical solutions of Eq. (1) for various regularly shaped bodies such as rectangular, cylindrical and spherical. Drying of many food products such as rice (Ece & Cihan, 1993), hazelnut (Demirtas, Ayhan, & Kaygusuz, 1998) and rapeseed (Crisp & Woods, 1994) has been successfully predicted using Fick’s second law with Arrhenius-type temperaturedependent diffusivity. The semi-theoretical models are generally derived by simplifying general series solutions of Fick’s second law or modification of simplified models and valid within the temperature, relative humidity, air flow velocity and moisture content range for which they were developed (Fortes & Okos, 1981). These models required small time compared to theoretical thin-layer models and do not need assumptions of geometry of a typical food, its mass diffusivity and conductivity (Parry, 1985). Among semi-theoretical thin-layer drying models, the two-term model (Eq. (2)), the Henderson and Pabis model (Eq.

This model was used successfully to model drying of corn (Henderson & Pabis, 1969), wheat (Watson & Bhargava, 1974) and peanut (Moss & Otten, 1989). The slope of this model, coefficient k0 ; is related to effective diffusivity when drying process takes place only in the falling rate period and liquid diffusion controls the process (Madamba, Driscoll, & Buckle, 1996). The Lewis model (Lewis, 1921) is a special case of the Henderson and Pabis model where intercept is unity. He described that the moisture transfer from the food products and agricultural material can be seen as analogous to the flow of heat from a body immersed in cool fluid. By comparing this phenomenon with Newton’s law of cooling, the drying rate is proportional to the difference in moisture content between the material being dried and the equilibrium moisture content at the drying air condition as: dM ¼ Àk0 ðM À Me Þ dt ð4Þ

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or after integrating yields MR ¼ M À Me ¼ expðÀk0 tÞ: M0 À Me ð5Þ

A0 from the initial conditions and k0 in the form of Arrhenius- and Power-type equations in the following way: In the Arrhenius type  Àa  2 k0 ¼ ða0 V a1 Þ exp ; T In the Power type k0 ¼ b0 T b1 V 2 : b Bruce (1985) also used this model to study the drying behaviour of barley. The Page model is a modification of the Lewis model to overcome its shortcomings. This model has produced good fits in predicting drying of grain and rough rice (Wang & Singh, 1978), white bean (Hutchinson & Otten, 1983), shelled corn (Agrawal & Singh, 1977) and barley (Bruce, 1985) MR ¼ M À Me ¼ expðÀk0 tn Þ: M0 À Me ð6Þ

ð10Þ

ð11Þ

Here T is the absolute temperature of the air (K), V is the air velocity (m/s), a0 ; a1 ; a2 ; b0 ; b1 and b2 are constants.

Overhults, White, Hamilton, and Ross (1973) also modified the Page model to describe the drying of soybean MR ¼ M À Me n ¼ expðÀk0 tÞ : M0 À Me ð7Þ

3. Materials and methods 3.1. Experiment design Fresh macerated tea, which grows in the Darjeeling Hills of India, was collected after the fermentation process. The macerated tea, after fermentation called Dhool, was well mixed and stored in a refrigerator in a sealed container for experiments. For drying experiments, a batch-type experimental dryer was designed and fabricated. A schematic diagram of a laboratory dryer is illustrated in Fig. 1. The dryer consists of three basic sections: air flow control section, heating control section, and sample platform. The control air flow was circulated in the dryer by a centrifugal fan, driven by a 1.5 kW, three-phase electric motor. The air flow rate was varied by adjusting a frequency modulator that controlled the rotational speed of the fan motor, and hence the fan speed. The air was heated while flowing through electric heating elements which were connected to a model TI series 305 controller from Texas instruments, USA. The controller was interfaced to a PC, which used a proportional-integral control algorithm to adjust the drying air temperature to a given set point.

The empirical models derive a direct relationship between average moisture content and drying time. They neglect the fundamentals of the drying process and their parameters have no physical meaning. Therefore, they cannot give a clear accurate view of the important processes occurring during drying although they may describe the drying curve for the conditions of the experiment (Keey, 1972). Among them the Thompson model (Eq. (8)) was used to describe the shelled corn drying (Thompson, Peart, & Foster, 1968) and the Wang and Singh model (Eq. (9)) was applied to study the intermittent drying of rough rice (Wang & Singh, 1978) t ¼ a lnðMRÞ þ bðlnðMRÞÞ ; and MR ¼ 1 þ at þ bt2 : ð9Þ
2

ð8Þ

The influence strength of the experimental drying variables is determined by the values of the model parameters,

Fig. 1. Schematic diagram of experimental laboratory dryer setup.

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The drying compartment of the test chamber had a swinging door, so that the cylindrical sample tray could be taken out or inserted back into the chamber. The sample tray, made entirely of stainless steel, had a perforated plate bottom. Concentric air distribution baffles fixed inside both transitions to the chamber provided uniform air flow. The air ducting and the test chamber were insulated to minimise heat losses from the system. Air conditions throughout each drying experiment were monitored on-line. The thermocouples and relative humidity probes were connected to a data logger, converting the analogue signals to digital outputs. The digital outputs were read by a personal computer through the data acquisition program. 3.2. Experimental procedure Experiments were performed to determine the effect of process variables on the thin-layer drying characteristics of black tea. The variables considered were the drying air temperature, absolute humidity, and air velocity. The change in absolute humidity was very low and later on it was neglected. By considering the actual drying range, a series of experiments were designed to cover as broad a spread of conditions as possible. Five temperature points were selected in the range 80–120°C by 10°C step. The experiments were conducted at different air velocities in the range 0.25–0.65 m/s by step of 0.20 m/s with constant air temperature at each. For estimation of the experimental error, 45 drying runs were performed in a systematic manner, serving as three replicates. Prior to placing the sample in the drying chamber, the system was run for at least one hour to obtain steady conditions. Once the temperature had stabilised and the air velocity was at the set value, the sample was placed on the sample holder and on-line data logging system was started. The flow of the heated air through the samples was set in the upward direction. Water loss from the samples was determined off-line. This was done by weighing the sample tray outside the chamber periodically using an electronic balance placed next to the test chamber. The accuracy of the weighing system was 0.001 g. The weighing procedure took not more than 15 s after removing the sample tray out from the chamber and this method is sufficiently accurate for generating reproducible drying curves. In the initial stages of each drying run, weights were recorded every minute, then every 2 min till the end point. The average moisture content of the samples for each weighing period was calculated based on the net mass of the samples (100 g) and the initial moisture content was determined before each experiment. The initial and final moisture contents were determined by a Sartorious moisture meter by drying the sample at 100°C. During the experiments, the dry- and wet-bulb temperatures of the air entering the

plenum chamber were measured on-line using thermocouples. The air velocity was measured by a hot wire anemometer with a reading accuracy of Æ0:05 m=s, the measurement location being 50 cm above the plenum of the test chamber. 3.2.1. Equilibrium moisture content The equilibrium moisture content of the black tea at different drying conditions used in the drying experiments was calculated using the following GAB equation form: ðaw Mm ckÞ ; ½ð1 À kaw Þð1 þ ckaw À kaw ފ   c1 c ¼ c0 exp ; RTab   k1 ; k ¼ k0 exp RTab Me ¼ ð12Þ ð13Þ ð14Þ

where Me is the equilibrium moisture content (% dry basis), aw is the water activity, and Tab is the absolute temperature (K) and R is the universal gas constant ð8:32 kJ molÀ1 KÀ1 Þ. The values of the constants c0 , k0 ; c1 and k1 are 0.02521, 0.99328, 14644.71 and 147.031, respectively (Panchariya, Popovic, & Sharma, 2001). 3.3. Data analysis procedure The collected data by on-line measurement as well as off-line were analysed using non-linear regression techniques. There are several criteria to evaluate the fitting of a model to experimental data. According to Noomhorm and Verma (1986) a model is good when the correlation coefficient (R2 ) is high and mean square error (MSE) is low. Other authors like Andriu, Stamatopolous, and Zafiropolous (1985); Chen and Morey (1989) and Palipane and Driscoll (1994), besides, use the mean relative deviation modulus ðP Þ. In this study, the nonlinear regression method was based on the Levenberg– Marquardt (LM) algorithm (Marquardt, 1963) and is the most widely used algorithm in non-linear least squares fitting. The LM algorithm, starting from some initial parameter values, minimises v2 by performing a series of iterations on the parameter values and computing v2 at each stage. In order to do this, first partial derivatives were calculated for all values of the input variables. The empirical coefficients can be estimated by fitting the total model employed to the experimental drying curves. The goodness of fit of the tested models to the experimental data are the coefficients of determination (COD, R2 ), the reduced v2 and the MSE between the experimental and calculated values for the tested models. The v2 can be described in equation form as

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N Á2 1 X À exp MRi À MRcal ; i N À n i¼1

353

v2 ¼

ð15Þ

where MRexp is the experimental moisture ratio at obi servation i; MRcal is the calculated moisture ratio at this i observation, N is the number of observations, and n is the number of constants. The lower the values of v2 , higher the value of coefficients of determination (R2 ) and lower the mean square of the MSE, which were chosen as the criteria for goodness of fit.

4. Results and discussion As the tea samples (Dhool) were collected at different times from the tea garden, it is obvious that the initial moisture content of all the runs was not the same. In order to normalise the drying curves, the data involving percentage dry basis moisture content versus time were transformed to dimensionless parameter called as moisture ratio versus time. Fig. 2 shows the typical characteristic drying curve (moisture ratio versus time) of black tea particles during thin-layer drying operation at different temperatures. The drying data were then fitted to the different semitheoretical models such as Lewis, Page, modified Page, two-term and Henderson and Pabis models, based on the ratios of the difference between the initial and final
Table 1 Statistical results obtained from different thin-layer drying models Model The Henderson and Pabis model T (°C) 80 90 100 110 120 80 90 100 110 120 80 90 100 110 120 80 90 100 110 120 80 90 100 110 120 R2 0.943 0.944 0.947 0.939 0.931 0.938 0.944 0.947 0.939 0.929 0.932 0.934 0.936 0.938 0.921 0.946 0.947 0.950 0.944 0.937 0.941 0.944 0.947 0.949 0.948 MSE 0.0048 0.0030 0.0026 0.0039 0.0184 0.0348 0.0030 0.0026 0.0038 0.0159 0.0047 0.0031 0.0024 0.0038 0.0159 0.0038 0.0030 0.0025 0.0035 0.0182 0.0048 0.0030 0.0026 0.0014 0.0026 v2 ðÂ10À4 Þ 1.2423 1.2078 0.9778 1.4722 8.3845 9.2404 1.2066 0.9826 3.4141 7.2558 1.2403 1.2065 1.9821 1.4131 7.2530 2.3094 1.3046 1.0042 1.4371 9.1006 1.2143 1.1630 0.9479 0.1499 1.0011

Fig. 2. Variation of moisture ratio with time at different temperatures and 0.45 m/s air velocity.

moisture contents and the equilibrium moisture content. The models were evaluated based on MSE, correlation coefficient (R2 ), and the v2 . The details of the statistical analysis are presented in Table 1. The Henderson and Pabis, the two-term, the Page and the modified Page models obtained a coefficient of determination (R2 ) greater than the acceptable R2 value of 0.93 at all drying air temperatures (Madamba et al.,

The Page model

The modified Page model

The two-term model

The Lewis model

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1996). The MSE and v2 values were below 0.018 and 9:0 Â 10À4 , respectively, for all drying air temperatures. Though, the MSE and coefficient of determination (R2 ) values for all the models were quite reasonable but the v2 values were greater than the values obtained by the Lewis model. Hence, the Lewis model gave better predictions than others, and satisfactorily described the thin-layer drying characteristics of Darjeeling black tea particles. The experimental results also illustrate the absence of constant drying period and drying takes place only in the falling rate period. This indicates that diffusion is the most likely physical mechanism governing moisture movement in the tea particles. The results were consistent with observations made by Temple and Boxtel (1999) who reported the absence of the constant rate period during drying of black tea (African variety). Thus, the drying kinetic data for each experimental run were interpreted using a Lewis model as discussed in the previous subsection. The variation of moisture ratio with time for each run was used for calculating the drying constant (k0 ) of the Lewis model using non-linear regression method. The coefficient of determination (R2 ), MSE and v2 between the experimental and calculated moisture ratios were obtained. The coefficient of determination (R2 ) was more than 0.93 in all the cases. Tables 2 and 3 illustrate the estimated values of the parameters involved with the Lewis model along with their corresponding coefficient of determination (R2 ) and mean square of deviations (MSE) with v2 between the experimental and calculated moisture ratios for each drying run. The results show the reasonability of the estimated data and experimental data. Figs. 3–6 show the details of the drying runs. 4.1. Effect of drying variables Based on the above results, the Arrhenius model was employed to examine the effect of other sample param-

Fig. 3. Variation of moisture ratio with time at different air velocities.

Fig. 4. Variation of drying constant ðkÞ with temperature at different air velocities.

eters like air temperature, absolute humidity, air velocity, and characteristic dimension on the thin-layer drying kinetics of black tea particles. The drying curves

Table 2 Results of non-linear regression analysis for empirical constants of the Lewis model Model The Lewis model T (°C) 80 90 100 110 120 k0 0.0017 0.0024 0.0030 0.0036 0.0046 R2 0.941 0.944 0.947 0.949 0.948 MSE 0.0048 0.0030 0.0026 0.0014 0.0026 v2 ðÂ10À4 Þ 1.2143 1.1630 0.9479 0.1499 1.0011

Table 3 Results of non-linear regression analysis for empirical constants of the Arrhenius and Power equations Equation Arrhenius Power Parameters a0 0.12563 b0 0.64801  10ðÀ7Þ a1 1.15202 b1 2.14815 a2 209.12341 b2 1.14635 R2 0.99869 0.9975 MSE 0.02318 0.03154 v2 ðÂ10À4 Þ 1.654 1.734

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locity has a significant influence on drying curves such as temperature. Fig. 4 illustrates the variation of drying constant (k0 ) with different temperatures and at different air velocities. From the above analyses, the external parameters (temperature and air velocity) have a great influence on drying rate and total drying takes place in the falling rate period only. The main cause behind this can be interpreted as the Dhool is nothing but the ruptured and cut portion of tea leaf, so the drying takes place not only by the epidermis of leaf but also from the cut portion of leaf as reported by Samejima and Yano (1985) in the case of shredded tobacco leaves. 4.2. Calculation of effective diffusivity and activation energy
Fig. 5. Experimental and predicted logarithmic moisture ratio at different drying times.

As described in previous subsections that the drying of black tea occurs in the falling rate period only and liquid diffusion controls the process. Fick’s second law can be used to describe the drying of black tea particles. General series solution of Fick’s second law in spherical coordinates is given below (Eq. (16)) in which constant diffusivity and spherical tea particle with a diameter of 0.0005 m were assumed   1 M À Me 6 X 1 n2 Deff p2 ¼ exp À t ; ð16Þ M0 À Me p2 n¼1 n2 R2 where D is the effective diffusivity (m2 /s) and R is the radius of the tea particles (m). The first term of Eq. (16) is also known as the Henderson and Pabis model. The slope, coefficient, k, of this model is related to the effective diffusivity k¼ Deff p2 : R2 ð17Þ

Fig. 6. Arrhenius-type relationship between effective diffusivity and temperature.

(moisture ratio versus drying time) for a range of values of a given variable by keeping the other variable constant were drawn and compared. Due to wetness of the Dhool, it is not possible to precisely separate the particles of different characteristic dimensions so this parameter was not included into the experimental study. For the range of experimental study, the absolute humidity had a smaller value and it had a negligible effect on the drying curve in comparison with other parameters. The influence of temperature on the thin-layer drying curve is shown in Fig. 2. The increase in temperature means the increase in drying rate and the figure shows as expected. Fig. 3 shows the effect of air velocity on the drying curve at constant temperature of 100°C. This can be interpreted as ‘‘at a constant temperature, increasing air velocity increases drying rate’’. Hence, the air ve-

The effective diffusivity was calculated by Eq. (17), using slopes derived from the linear regression of lnðMRÞ against time data shown in Fig. 5. Generally, an effective diffusivity is used due to limited information on the mechanism of moisture movement during drying and complexity of the process. The effective diffusivities (Deff ) during drying of tea particles varied from 1:141 Â 10À11 to 2:985 Â 10À11 (m/s) in the temperature range from 80°C to 120°C. Rizvi (1986) stated that effective diffusivities depend on the drying air temperature besides variety and composition of the material. The heat of sorption which is a measure of moisture mobility within the food is another factor that affects effective diffusivity (Madamba et al., 1996). Effect of temperature on effective diffusivity is generally described using Arrhenius-type relationship to obtain better agreement of the predicted curve with experimental data (Crisp & Woods, 1994; Henderson, 1974; Madamba et al., 1996). Crisp and Woods (1994)

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P.C. Panchariya et al. / Journal of Food Engineering 52 (2002) 349–357 Agrawal, Y. C., & Singh, R. P. (1977). Thin layer studies on short grain rough rice. Transactions of ASAE, 77, 3531. Basunia, M. A., & Abe, T. (2001). Thin layer solar drying characteristics of rough rice under natural convection. Journal of Food Engineering, 47, 295–301. Bruce, D. M. (1985). Exposed-layer barley drying, three models fitted to new data up to 150°C. Journal of Agriculture Engineering Research, 32, 337–347. Can, A. (2000). Drying kinetic of pumpkinseeds. International Journal of Energy Research, 24, 965–975. Carbonell, J. V., Pinaga, F., Yusa, V., & Pena, J. L. (1986). Dehydration of paprika and kinetics of colour degradation. Journal of Food Engineering, 5, 179–193. Chen, C., & Morey, R. V. (1989). Comparison of four ERH/EMC equation. Transactions of ASAE, 32(3), 983–990. Crank, J. (1975). The mathematics of diffusion. Oxford, England: Claredon Press. Crisp, J., & Woods, J. L. (1994). The drying properties of rapeseed. Journal of Agriculture Engineering Research, 57, 89–97. Demirtas, C., Ayhan, T., & Kaygusuz, K. (1998). Drying behavior of hazelnuts. Journal of the Science of Food and Agriculture, 76, 559– 564. Ece, M. C., & Cihan, A. (1993). A liquid diffusion model for drying rough rice. Transactions of ASAE, 15, 156–159. Fortes, M., & Okos, M. R. (1981). Non-equilibrium thermodynamics approach to heat and mass transfer in corn kernels. Transactions of ASAE, 22, 761–769. Henderson, S. M. (1974). Progress in developing the thin layer drying equation. Transactions of ASAE, 17, 1167–1172. Henderson, S. M., & Pabis, S. (1969). Grain drying theory I. Temperature effect on drying coefficient. Journal of Agriculture Engineering Research, 6(3), 169–174. Hutchinson, D., & Otten, L. (1983). Thin layer air drying of soybeans and white beans. Journal of Food Technology, 18, 507–524. Keey, R. B. (1972). Drying: principles and practice. New York: Pregoman Press. Kiranoudis, C. T., Maroulis, Z. B., Tasami, E., & Marinos-Kouris, D. (1997). Drying kinetics of some fruits. Drying Technology, An International journal, 15(5), 1399–1418. Lewis, W. K. (1921). The rate of drying of solids materials. Industrial Engineering Chemistry, 13, 427. Lopez, A., Iguaz, A., Esnoz, & Virseda, P. (2000). Thin-layer drying behaviour of vegetable waste from wholesale market. Drying Technology, An International Journal, 18(4&5), 995–1006. Madamba, P. S., Driscoll, R. H., & Buckle, K. A. (1996). Thin layer drying characteristics of garlic slices. Journal of Food Engineering, 29, 75–97. Marquardt, D. W. (1963). An algorithm for least square estimation of non-linear parameters. Journal of the Society for Industrial and Applied Mathematics, 2, 431–441. Mazza, G., & Le Maguer, M. (1980). Dehydration of onion: some theoretical and pratical considerations. Journal of Food Technology, 15, 181–194. Moss, J. R., & Otten, L. (1989). A relationship between color development and moisture content during roasting of peanut. Canadian Institute of Food Science and Technology Journal, 22, 34–39. Noomhorm, A., & Verma, L. R. (1986). Generalised single layer rice drying models. Transactions of ASAE, 29(2), 587. Overhults, D. G., White, G. M., Hamilton, H. E., & Ross, I. J. (1973). Drying soyabeans with heated air. Transactions of ASAE, 16, 112– 113. Palipane, K. B., & Driscoll, R. H. (1994). The thin layer drying characteristics of Macadamia in-shell nuts and kernels. Journal of Food Engineering, 23, 129–144. Panchariya, P. C., Popovic, D., & Sharma, A. L. (2001). Modelling of desorption isotherm of black tea. Drying Technology, An International Journal, 19(5) (in press).

reasoned that temperature is not a function of radial position in the grain under normally experienced drying conditions, and diffusivity varies more with temperature than moisture content   Ea Deff ¼ D0 exp À ; ð18Þ RTa where D0 is a diffusivity constant equivalent to the diffusivity at infinitely high temperature and Ea is the activation energy (kJ/kg). The logarithm of Deff as a function of the reciprocal of absolute temperature (Ta ) is plotted in Fig. 6. The results show a linear relationship between (log Deff ) and ð1=Ta Þ or an Arrhenius-type relationship (Eq. (18)). The diffusivity constant (D0 ) and activation energy (Ea ) calculated from the linear regression are 1:68 Â 10À7 ðm2 =sÞ and 406.028 (kJ/mol), respectively. It is higher than the activation energy of vegetable waste drying (19.8 kJ/mol) (Lopez, Iguaz, Esnoz, & Virseda, 2000) and lower than the activation energies of onion drying (1200 kJ/kg) (Mazza & Le Maguer, 1980) and paprika drying (2036 kJ/kg) (Carbonell, Pinaga, Yusa, & Pena, 1986). 5. Conclusions An experimental dryer system was designed and constructed, and operated well when used to establish thin-layer drying curves on black tea under a wide range of drying conditions similar to those in actual industrial black tea drying operations. The Lewis model adequately described the single-layer drying behaviour of black tea particles. Temperature dependence of the diffusivity coefficients was described by an Arrhenius-type relationship. The activation energy for moisture diffusion was found to be 406.02 kJ/mol. The drying rate constant was correlated well with the experimental drying variables like hot air velocity and hot air temperature using the non-linear polynomial regression model. The drying rate constant was greatly influenced by the air velocity and the air temperature. Further research about the effect of initial moisture content, air relative humidity and layer thickness on drying characteristics is necessary for the optimisation of black tea drying process. Acknowledgements The authors gratefully acknowledge DAAD, Bonn, Germany for their financial support to carry out this study.

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